Problem: Solve for $x$ and $y$ using elimination. ${-x-3y = -15}$ ${x+5y = 21}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $2y = 6$ $\dfrac{2y}{{2}} = \dfrac{6}{{2}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {-x-3y = -15}\thinspace$ to find $x$ ${-x - 3}{(3)}{= -15}$ $-x-9 = -15$ $-x-9{+9} = -15{+9}$ $-x = -6$ $\dfrac{-x}{{-1}} = \dfrac{-6}{{-1}}$ ${x = 6}$ You can also plug ${y = 3}$ into $\thinspace {x+5y = 21}\thinspace$ and get the same answer for $x$ : ${x + 5}{(3)}{= 21}$ ${x = 6}$